An Interactive Method for Solving Multiple Objective Quadratic-Linear Programming Models

In this paper, we describe an interactive procedure for solving multiple criteria problems with one quadratic objective, several linear objectives, and a set of linear constraints. The procedure is based on the use of reference directions and weighted-sums. The reference directions for the linear functions, and the weighted-sums for combining the quadratic function with the linear ones are used as parameters to implement the free search of nondominated solutions. This idea leads to the parametric linear complementarity problem formulation. An approach to deal with this type of problems is given as well. The approach is illustrated with a numerical example.